a nice problem on transformation

[Tahmid Hasan]

Let $ABC$ be a triangle and $H$ its orthocenter.Denote by $A_1,B_1,C_1$ the centers of the circles circumscribed about the triangles $CHB,CHA,AHB$ respectively.
Prove that the $\triangle ABC$ is congruent to $\triangle A_1B_1C_1$ and that the nine-point
circle of $\triangle ABC$ is also the nine-point circle of $\triangle A_1B_1C_1$.